Work, Power & Energy — JEE Main PYQs

A body of mass 2 kg begins to move under the action of a time dependent force given by $\overrightarrow{\mathrm{F}}=\left(6\mathrm{t}\hat{\mathrm{i}}+6{\mathrm{t}}^2\hat{\mathrm{j}}\right)\mathrm{N}$. The power developed by the force at the time t is given by:

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\mathrm{m}/\mathrm{s}$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $\_\_\_\_$ cm.

A body of mass 5 kg is moving with a momentum of $10\mathrm{kg}{\mathrm{ms}}^{-1}$. Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is $\_\_\_\_$ J.

The momentum of a body is increased by $50\%$. The percentage increase in the kinetic energy of the body is ____ %

A body is dropped on ground from a height '$h_1$' and after hitting the ground, it rebounds to a height '$h_2$'. If the ratio of velocities of the body just before and after hitting ground is 4, then percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ …

If the maximum load carried by an elevator is 1400 kg (600 kg - Passenger + 800 kg - elevator), which is moving up with a uniform speed of $3{\mathrm{ms}}^{-1}$ and the frictional force acting on it is 2000 N, then the maximum power used by the motor is ______ $\mathrm{kW}$ ( …

A closed circular tube of average radius 15 cm , whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is $22\mathrm{m}/\mathrm{s}$, when it is introduced at the top of tube. After completing five oscillati …

A force $\overrightarrow{\mathrm{F}}=(2+3\mathrm{x})\hat{\mathrm{i}}$ acts on a particle in the x direction where F is in newton and x is in meter. The work done by this force during a displacement from $\mathrm{x}=0$ to $\mathrm{x}=4\mathrm{m}$, is ____ J.

Given below are two statements:

Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.

Statement II : A car moving towards east takes a turn and moves towar …

To maintain a speed of $80\mathrm{km}/\mathrm{h}$ by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be
____ KJ. [The coefficient of friction between tyre of bus and road is 0.04].

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x}+1}$, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

A car accelerates from rest to $u\mathrm{m}/\mathrm{s}$. The energy spent in this process is E J. The energy required to accelerate the car from $u\mathrm{m}/\mathrm{s}$ to $2u\mathrm{m}/\mathrm{s}$ is nE J. The value of $n$ is $\_\_\_\_$.

A block of mass 10 kg is moving along x-axis under the action of force $F=5x$ N. The work done by the force in moving the block from $x=2$ m to 4 m will be ______ J.

A particle of mass 10 g moves in a straight line with retardation 2 x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is ${\left(\frac{10}{x}\right)}^{-n}$ J. The value of $n$ will be

A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation $\mathrm{v}=10\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$ the force acting on the body is:-

A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ }$ with horizontal with an affective acceleration of 1 ${\mathrm{ms}}^{-2}$. The power delivered by the pulling force at $\mathrm{t}=10\mathrm{s}$ from the start is $\_\_\_\_$ …

A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k}\mathrm{N}$. The value of work done will be ____ J.

A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F}=\left(t\hat{i}+3t^2\hat{j}\right)$ N, where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. The power developed by above force, at the time $t=2$ s, will be ______ W.

An object of mass '$m$' initially at rest on a smooth horizontal plane starts moving under the action of force $\mathrm{F}=2\mathrm{N}$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as …

Identify the correct statements from the following:
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Wor …

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is $\frac{1}{3}{\alpha }^2\sqrt{P}$ m. The value of $\alpha$ will be ......

A lift of mass $\mathrm{M}=500\mathrm{kg}$ is descending with speed of $2{\mathrm{ms}}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2{\mathrm{ms}}^{-2}$. The kinetic energy of the lift at the end of fall through to a dista …

A force $F=(5+3y^2)$ acts on a particle in the y direction, where F is newton and y is in meter. The work done by the force during a displacement from $y=2\text{m}$ to $y=5\text{m}$ is ______ J.

If momentum of a body is increased by $20\%$, then its kinetic energy increases by :

A block of mass '$m$' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be $nE$ Nm${}^{-1}$ for $n$ = _____.

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

Two cylindrical vessels of equal cross-sectional area $16{\mathrm{cm}}^2$ contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Tak …

A body of mass 0.5 kg travels on straight line path with velocity $\mathrm{v}=(3{\mathrm{x}}^2+4)\mathrm{m}/\mathrm{s}$. The net workdone by the force during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=2\mathrm{m}$ is :

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+\mathrm{x})$ cm inside the block. The value of $x$ …

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of 4 ms⁻¹, is. ______ cm.
(take g=10 ms⁻²)

As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant $2{\mathrm{Nm}}^{-1}$. If both are given velocity v in opposite directions, then maximum elongation of the spring is :

A block of mass 2 kg moving on a horizontal surface with speed of $4{\mathrm{ms}}^{-1}$ enters a rough surface ranging from $\mathrm{x}=0.5\mathrm{m}$ to $\mathrm{x}=1.5\mathrm{m}$. The retarding force in this range of rough surface is related to distance by …

Water fall from a 40 m high dam at the rate of $9\times 10^4\mathrm{kg}$ per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is:
(Take …

A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of change in its velocity, as it reaches a position where th …

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.

The velocity of centre of mass of the wheel when it reaches at the bottom Q of the …

A particle of mass m is moving in a circular path of constant radius $r$ such that its centripetal acceleration (a) is varying with time t as $\mathrm{a}={\mathrm{k}}^2{\mathrm{rt}}^2$. where k is a constant. The power delivered to the particle by the force acting on it is given …

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at $60^{\circ }$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ______ …

In the given figure, the block of mass $m$ is dropped from the point ' A '. The expression for kinetic energy of block when it reaches point ' B ' is :

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of $6.0\times 10^5{\mathrm{ms}}^{-1}$. The speed with which electron enters the p side will be $\frac{x}{3}\times 10^5{\mathrm{ms}}^{-1}$ the value of x i …

Arrange the four graphs in descending order of total work done; where ${\mathrm{W}}_1,{\mathrm{W}}_2,{\mathrm{W}}_3$ and ${\mathrm{W}}_4$ are the work done corresponding to figure $\mathrm{a},\mathrm{b},\mathrm{c}$ and d respectively.

Figure-a

Figure-b

Figure-c

Fi …

A particle of mass 500 gm is moving in a straight line with velocity $v=b{x}^{5/2}$. The work done by the net force during its displacement from $x=0$ to $x=4$ m is: (Take $b=0.25{\mathrm{m}}^{-3/2}{\mathrm{s}}^{-1}$).

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength $1\times 10^5{\mathrm{NC}}^{-1}$. If the charge on the particle is $40\mu \mathrm{C}$ and the initial velocity is $200{\mathrm{ms}}^{-1}$, how much distance it will tra …

A particle experiences a variable force $\vec{F}=\left(4x\hat{i}+3y^2\hat{j}\right)$ in a horizontal $x-y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $\mathrm{x}-\mathrm{y}$ plane, the Kin …

A ball of mass 100 g is dropped from a height $h=10$ cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is ______ ${\text{Nm}}^{-1}$. (Use …

Potential energy as a function of r is given by $U=\frac{A}{r^{10}}-\frac{B}{r^5}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

A 0.5 kg block moving at a speed of $12{\mathrm{ms}}^{-1}$ compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be ______ ${\mathrm{Nm}}^{-1}$.

A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of $k$ is ______ (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

A particle is projected with velocity ${\mathrm{v}}_0$ along x -axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. $\mathrm{ma}=-\alpha {\mathrm{x}}^2$. The distance at which the particle stops:

Two solids $A$ and $B$ of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies $(\text{ K.E }{)}_A:(\text{ K.E }{)}_B$ will be $\frac{A}{1}$, so the value of $A$ will be ______

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :